Question

prove 4i/√61 -3j/√61 +6k/√61 is a unit vector



solve in clear steps​

Answer 1

The Reqd. Unit Vector =(6√61,−3√61, -4✓61) .

Explanation:

Let a non-null vector

→

x be given. Then, a unit vector parallel to

→

x is denoted by

ˆ

x and is defined by,

ˆ

x=

→

x/∣|→x |∣

→

A=2^i−6ˆj−3ˆk

=(2,−6,−3),

&,

→

B=(4,3,−1).

Hence, the Resultant of

→Aand→B , is

→A+→B , & is, →A+→B=

(2,−6,−3)+(4,3,−1)

=(2+4,−6+3,−3−1)

=(6,−3,−4)

∴

∣|→A+→B | | =

$\sqrt{ {6}^{2} + ( { - 3)}^{2 } + {( - 4)}^{2} }$

Hence, the Reqd. Unit Vector =

→A+→B/∣∣→A+→B∣∣

$\frac{1}{ \sqrt{61} } \times (6. \: - 3. \: - 4. \: ) = \frac{6}{ \sqrt{61} } . \: \frac{ - 3}{ \sqrt{61} } . \: \frac{ - 4}{ \sqrt{61} }$

${\huge{HOPE \: IT \: HELPS}}$

Answer 2

Explanation:

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